Calculation method for tension, bending rigidity and rotational rigidity at both ends of a linear body

Abstract

To provide a method for calculating the tension and the like of each of two linear bodies gripped by a gripping device in a cross section.SOLUTION: There is disclosed a method for calculating the tension and the like of each of two linear bodies gripped by a gripping device in a cross section. The calculation method comprises: an actual measurement step of obtaining actually measured values of characteristic frequencies in plural modes; and a calculation step of calculating the tension and the like by using a calculation reference expression set by using a boundary condition expressing that a cross section of two linear bodies is gripped by a gripping device and both ends of each of the two linear bodies have the rotational rigidity and the actually measured values of the characteristic frequencies in the plural modes.SELECTED DRAWING: Figure 4

Description

[Technical field]

[0001] The present invention relates to a method for calculating the tension, bending stiffness and rotation stiffness at both ends of two linear bodies held by a holding device so as to cross each other. [Background technology]

[0002] Various methods have been proposed for calculating tension acting on linear bodies such as bridge cables, string beams, and electric wires (see Patent Documents 1 and 2). In these methods, the natural frequency of a cable modeled as a one-dimensional beam is calculated, and the calculated natural frequency is compared with the actual measured natural frequency appearing in vibration data obtained by applying an impact to an actual cable. The cable tension is calculated based on the results of this comparison. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 9-101289 [Patent Document 2] Japanese Patent Application Publication No. 11-271155 Summary of the Invention [Problem to be solved by the invention]

[0004] The above-mentioned calculation method using a one-dimensional beam model can be suitably used to calculate the tension of a single linear body. However, even if the above-mentioned calculation method is applied to a structure in which two linear bodies are arranged crossing each other and the intersection of these linear bodies is gripped by a gripping device, only the tension is calculated under a state in which these linear bodies move independently at the intersection. In other words, the conventional tension calculation method cannot obtain a highly accurate calculated value of tension due to the influence of the linear bodies being mutually constrained at the intersection.

[0005] An object of the present invention is to provide a method for calculating the tension, bending rigidity, and rotational rigidity at both ends of two linear bodies held by a holding device so as to cross each other. [Means for solving the problem]

[0006] A calculation method according to one aspect of the present invention can be used to calculate the tension, bending rigidity, and rotational rigidity at both ends of two linear bodies held by a holding device so as to cross each other. The calculation method includes a measurement step of obtaining actual measured values ​​of natural frequencies of multiple modes for each of the two linear bodies based on the vibration of the two linear bodies, and a calculation step of calculating the tension, bending rigidity, and rotational rigidity using a calculation standard formula set using boundary conditions that represent that the intersection of the two linear bodies is held by the holding device and that both ends of each of the two linear bodies have the rotational rigidity, and the actual measured values ​​of the natural frequencies of the multiple modes. The calculation standard formula is expressed as an equation in which a function including variables of the tension, bending rigidity, rotational rigidity, and the natural frequencies of the multiple modes is equal to a predetermined value. In the calculation process, candidate values ​​set for the tension, bending stiffness, and rotational stiffness, and the actual measured values ​​of the natural frequencies of the multiple modes are substituted into corresponding variables of the function to obtain calculated values ​​of the function, and the tension, bending stiffness, and rotational stiffness are calculated based on a comparison between the obtained calculated values ​​and the specified values.

[0007] In the above-described configuration, the calculation standard equation used in the calculation step for calculating tension and the like is set using the following two boundary conditions. The intersection of the two linear bodies is held by a holding device. -Both ends of each of the two linear bodies have rotational rigidity.

[0008] Since the boundary condition that the intersection of the two linear bodies is gripped by the gripping device is used, the calculation standard formula can represent the vibration mode in which the two linear bodies vibrate integrally at the intersection. Furthermore, since the rotational rigidity represents the resistance of the linear body to bending at both ends, the calculation standard formula set using the boundary condition can represent the degree of constraint against bending at both ends of the linear body in an actual structure.

[0009] The calculation standard formula set using the above-mentioned boundary conditions is expressed as a formula in which a function including variables of tension, bending stiffness, rotation stiffness, and natural frequencies of multiple modes is equal to a predetermined value. The closer the calculated value obtained by substituting numerical values ​​into these variables is to the above-mentioned predetermined value, the closer the substituted numerical value is to the true value that satisfies the calculation standard formula. For this reason, in the calculation process, candidate values ​​of tension, bending stiffness, and rotation stiffness, and actual measured values ​​of natural frequencies of multiple modes are substituted into the corresponding variables. By comparing the calculated value obtained by this substitution process with the predetermined value taken by the function of the calculation standard formula, it is possible to know whether the substituted candidate value is close to the true value that satisfies the calculation standard formula. In particular, in the above-mentioned calculation method, the substitution process is performed using the rotation stiffness as a variable, and the tension, etc. can be calculated taking into account the degree of constraint against bending at both ends of the linear body. Therefore, the calculated tension, etc. have high accuracy.

[0010] With respect to the above-mentioned configuration, the calculation criteria equation may express the relationship between the natural frequencies, the tension, the bending stiffness, and the rotational stiffness of the multiple modes without including a modal order.

[0011] In the calculation methods of tensions and the like in Patent Documents 1 and 2, it is necessary to assign the measured values ​​of natural frequencies of multiple modes to the mode orders in correspondence with each other. However, it is assumed that the correspondence between the natural frequencies and the mode orders is performed incorrectly. For example, if a natural frequency with a mode order of 3 is overlooked, a natural frequency with a mode order of 4 may actually be acquired as a natural frequency with a mode order of 3. In this case, 3 may be assigned to the variable of the mode order in the calculation formula in Patent Documents 1 and 2, while a natural frequency with a mode order of 4 may be assigned to the variable of the natural frequency in the calculation formula. If such an incorrect assignment process is performed, the tensions and the like of the linear body cannot be calculated with high accuracy.

[0012] On the other hand, the above-mentioned calculation method uses a calculation standard formula that does not include the mode order, so that the actual measured value of the natural frequency of the linear body can be substituted into the function of the calculation standard formula without being associated with the mode order, thereby preventing the above-mentioned erroneous substitution process.

[0013] With regard to the above-described configuration, the boundary condition may include a condition indicating that the displacement directions and displacement amounts of the two linear bodies at the intersection are equal.

[0014] When the two linear bodies apply an impact to a structure held by a holding device at an intersection, the displacements (i.e., the displacement direction and the displacement amount) of the two linear bodies at the intersection are equal to each other. In the above-mentioned configuration, the boundary condition that the displacements (i.e., the displacement direction and the displacement amount) of the two linear bodies are equal is used, so that it is possible to calculate the tensions of the two linear bodies held by the holding device at the intersection.

[0015] Regarding the above-mentioned configuration, the function of the calculation reference formula may express the sum of the force acting on the intersection of one of the two linear bodies and the force acting on the intersection of the other linear body, using variables of the natural frequency of the multiple modes, the tension, the bending stiffness, and the rotation stiffness. The calculation reference formula may be expressed as an equation in which the function is equal to a value of zero. In the calculation step, the candidate values ​​of the tension, the bending stiffness, and the rotation stiffness, and the actual measured value of the natural frequency of the multiple modes may be substituted for the corresponding variables of the function, respectively, to obtain the calculated value. The tension, the bending stiffness, and the rotation stiffness may be calculated based on a comparison between the obtained calculated value and the value of zero.

[0016] In the above-mentioned configuration, the two linear bodies are held by the holding parts at their intersections, so that the forces acting on these linear bodies at the intersections are balanced. That is, the sum of the force acting on one linear body at the intersection and the force acting on the other linear body at the intersection is equal to zero, and this balance of forces is expressed by the calculation standard formula. The force acting on the intersections can be expressed as a function including variables of tension, bending rigidity, rotational rigidity, and natural vibration frequencies of multiple modes. It can be seen that the closer the calculated value obtained from the function by substituting numerical values ​​for these variables is to zero, the closer the substituted numerical values ​​are to the conditions under which the balance of forces at the intersections is established. For this reason, in the calculation step, the tension, etc. are calculated by comparing the calculated value obtained by the substitution process with the value of zero.

[0017] With regard to the above-mentioned configuration, in the actual measurement step, Fourier amplitudes at the natural frequencies of the multiple modes corresponding to the actual values ​​of the natural frequencies of the multiple modes are measured at two different positions on each of the two linear bodies, and an actual value of a Fourier amplitude ratio, which is a ratio of the actual values ​​of the Fourier amplitudes obtained at the two positions, is obtained. The function of the calculation standard formula is set to represent the difference between a theoretical value obtained from a theoretical formula of the Fourier amplitude ratio expressed as a function of the tension, the bending rigidity, the rotational rigidity, and the natural frequencies of the multiple modes, and the actual value of the Fourier amplitude ratio. The calculation standard formula is set to represent a relationship in which the difference between the theoretical value of the Fourier amplitude ratio and the actual value of the Fourier amplitude ratio is equal to a zero value. In the calculation step, the actual value of the Fourier amplitude ratio acquired in the actual measurement step is substituted into the term of the actual value of the Fourier amplitude ratio in the function, and the candidate values ​​of the tension, the bending rigidity, and the rotational rigidity, and the actual values ​​of the natural frequencies of the multiple modes are substituted into the theoretical formula to obtain the difference between the actual value of the Fourier amplitude ratio and the theoretical value of the Fourier amplitude ratio as the calculated value, and the tension, the bending rigidity, and the rotational rigidity are calculated based on a comparison between the calculated value related to the difference and the value of zero.

[0018] The theoretical formula of the Fourier amplitude ratio can be expressed as a function of tension, bending stiffness, rotation stiffness, and natural frequencies of multiple modes. In the above-mentioned configuration, the theoretical value of the Fourier amplitude ratio is calculated by substituting the candidate values ​​of tension, bending stiffness, and rotation stiffness and the actual measured values ​​of the natural frequencies of multiple modes into this theoretical formula. If this theoretical value is close to the actual measured value of the Fourier amplitude ratio, the calculated value, which is the difference between the actual measured value and the theoretical value of the Fourier amplitude ratio, is close to zero. Therefore, by comparing the calculated value with zero, it is possible to know whether the candidate values ​​of tension, bending stiffness, and rotation stiffness substituted into the theoretical formula are close to the true values ​​that establish the calculation standard formula.

[0019] With regard to the above-described configuration, in the calculation step, another candidate value set for at least one of the tension, the bending stiffness, and the rotational stiffness, and the actual measured values ​​of the natural frequencies of the multiple modes are substituted into the function to obtain another calculated value, thereby obtaining a plurality of calculated values, and the candidate value that is closest to the predetermined value among the plurality of calculated values ​​may be determined as the calculated value of the tension, the bending stiffness, and the rotational stiffness.

[0020] In the above-mentioned calculation method, multiple candidate values ​​are substituted into the function of the calculation standard formula, so that multiple calculated values ​​are obtained. Among these calculated values, the candidate value obtained that is close to the predetermined value when the calculation standard formula is satisfied is relatively close to the true value that satisfies the calculation standard formula. Since such a candidate value is determined as the calculated value of tension, etc., the accuracy of the calculated value of tension, etc. is improved.

[0021] Regarding the above-mentioned configuration, in the calculation step, a substitution process may be repeated to substitute another candidate value set for at least one of the tension, the bending stiffness, and the rotational stiffness, and the actual measured values ​​of the natural frequencies of the multiple modes into the function, until a difference between the calculated value and the specified value becomes less than a specified threshold value.

[0022] In the above-mentioned calculation method, in order to guarantee the accuracy of the calculated value of tension, etc., a threshold is set for the difference between the calculated value and a predetermined value when the calculation reference formula is satisfied. The substitution process is repeated until the difference between these values ​​becomes less than the threshold, so that the calculated value of tension, etc. has the accuracy guaranteed by the threshold. Effect of the Invention

[0023] The technique described above makes it possible to calculate the tension and bending stiffness of each of two linear bodies gripped by a gripping device so that they cross each other. [Brief description of the drawings]

[0024] [Figure 1] FIG. 1 is a schematic diagram of a structure having two crossed cables. [Diagram 2] FIG. 1 is a schematic diagram of a vibration model in which a cable is modeled as a one-dimensional beam. [Diagram 3] FIG. 1 is a schematic diagram of forces acting around a cable intersection. [Figure 4] 10 is a schematic flowchart of a method for calculating tension and the like. [Diagram 5] This data was obtained by performing a Fourier transform on the time history response values ​​of the cable vibration. [Figure 6] 1 is a graph showing a method for searching for an optimal solution based on the MultiStart method. [Figure 7] This data was obtained by performing a Fourier transform on the time history response values ​​of the cable vibration. [Figure 8] 10 is a schematic flowchart of a method for calculating tension and the like. [Figure 9] FIG. 1 is a schematic diagram of a structure having two crossed cables. [Figure 10] 10 is a schematic flowchart of a method for calculating tension and the like. [Figure 11] This data was obtained by performing a Fourier transform on the time history response values ​​of the cable vibration. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0025] 1 is a schematic plan view of a structure 100 having two cables 121 and 122 (linear bodies) crossing each other. The cables 121 and 122 are fixed in a tensioned state. Both ends of the cables 121 and 122 are supported with a predetermined rotational rigidity.

[0026] A gripping device 130 is attached to the intersection of the cables 121, 122. The gripping device 130 is configured to grip the cables 121, 122 at the intersection of the cables 121, 122. Therefore, at the intersection, the vibration amplitude and vibration direction of both cables 121, 122 are equal.

[0027] The cables 121 and 122 are each divided into two spans by the gripping device 130 attached to the intersection. In the following description, the length of the cable 121 from the left end of the cable 121 to the gripping device 130 in FIG. 1 is referred to as "span 171." In the following description, the length of the cable 121 from the right end of the cable 121 to the gripping device 130 in FIG. 1 is referred to as "span 172." In the following description, the length of the cable 121 from the left end of the cable 122 to the gripping device 130 in FIG. 1 is referred to as "span 173." In the following description, the length of the cable 122 from the right end of the cable 121 to the gripping device 130 in FIG. 1 is referred to as "span 174."

[0028] An acceleration sensor 141 is attached to span 171 of cable 121, and an acceleration sensor 143 is attached to span 173 of cable 122. Acceleration sensors 141, 143 are configured to detect the acceleration of vibrations generated in cables 121, 122 due to an impact given to at least one of cables 121, 122. In this embodiment, cables 121, 122 are vibrated in a direction perpendicular to a plane including cables 121, 122 (direction perpendicular to the paper surface of FIG. 1). In the following description, the direction perpendicular to the plane including cables 121, 122 is referred to as the "out-of-plane direction."

[0029] The acceleration sensors 141, 143 are electrically connected to a data collection device 160 (for example, a personal computer), and acceleration data acquired by the acceleration sensors 141, 143 is accumulated in the data collection device 160 as time history response values. The data collection device 160 is configured to perform a predetermined analysis process on the acceleration data, and data on the actual measured values ​​of the natural frequencies (natural frequencies in the out-of-plane direction) of the cables 121, 122 is obtained through this analysis process. Based on the obtained data on the natural frequencies, the tensions, etc. of the cables 121, 122 are calculated.

[0030] <Derivation of the calculation standard formula> In order to calculate the tensions, etc. of the cables 121, 122, a calculation standard formula based on the vibration equation for the cables 121, 122 is derived. The calculation standard formula is expressed as a formula in which a function including variables such as tensions is equal to a predetermined value. Using the predetermined value taken by the function of the calculation standard formula as a standard, it is determined whether the calculated values ​​of tensions, etc. obtained by the calculation processing described below are close to true values.

[0031] The calculation formula can be set by modeling each of the cables 121 and 122 as a one-dimensional beam supported at both ends with a predetermined rotational stiffness, as shown in FIG. 2. In FIG. 2, the subscript k takes a value of 1 or 2. When the subscript k takes a value of 1, the model in FIG. 2 refers to the cable 121 in FIG. 1. When the subscript k takes a value of 2, the model in FIG. 2 refers to the cable 122 in FIG. 1. In the following description, the term "cable k" refers to one of the cables 121 and 122. That is, when "k" takes a value of 1, the term "cable k" refers to the cable 121, and when "k" takes a value of 2, the term "cable k" refers to the cable 122.

[0032] In the model of FIG. 2, a rotational spring is inserted at both ends of cable k to indicate that both ends of cable k have a certain rotational stiffness. The rotational stiffness at both ends of cable k is the stiffness of the rotational spring (i.e., the rotational spring stiffness K k ) is represented as

[0033] In Fig. 2, an intersection 131 is shown on the cable k. The intersection 131 refers to the portion where the cables 121 and 122 intersect (i.e., the gripping position of the gripping device 130 in Fig. 1). In the following description, the length of the span from the left end of the cable k to the intersection 131 (i.e., the spans 171 and 173 of the cables 121 and 122) is defined as L k1 The length of the span from the other end of the cable k to the intersection 131 (i.e., the spans 172 and 174 of the cables 121 and 122) is L k2 The total length of cable k (L k1 +L k2) to L k Let us assume that.

[0034] In Figure 2, the left end of cable k is the origin and x extends to the right. k1 axis and the right end of cable k as the origin, x extending to the left k2 The direction perpendicular to the paper surface of FIG. 2 is defined as the out-of-plane direction, and the displacement of cable k in this direction is defined as w kd The subscript d is used to indicate the span of cable k and takes the value of 1 or 2. Subscript d with a value of 1 indicates the left span of cable k. Subscript d with a value of 2 indicates the right span of cable k. That is, the displacement "w 11 " indicates the amount of displacement of the span 171 of the cable 121 in the out-of-plane direction. 12 " indicates the amount of displacement of the span 172 of the cable 121 in the out-of-plane direction. 21 " indicates the amount of displacement of the span 173 of the cable 122 in the out-of-plane direction. 22 " indicates the amount of displacement of span 174 of cable 122 in the out-of-plane direction.

[0035] The vibration equation of cable k at time t is given as follows: Note that the mass of the gripping device 130 is not taken into account.

[0036]

number

[0037] When the above vibration equation (Equation 1) is solved by the variable separation method, the following relational expression is obtained.

[0038]

number

[0039] Using this relation (equation 2), the vibration equation of "equation 1" can be rewritten as follows:

[0040]

number

[0041] The general solution to the vibration equation in "Equation 3" is expressed as follows.

[0042]

number

[0043] Both ends of cable k (x kd = 0), no displacement of cable k occurs, and both ends of cable k have a rotational spring stiffness K k Since a rotational spring having the following torque is inserted, the following boundary conditions are established for the displacement and bending moment at both ends of the cable k. The following boundary conditions for the bending moment indicate that both ends of the cables 121 and 122 have torque rigidity.

[0044]

number

[0045] Cable k intersection 131(x k1 =L k1 ,x k2 =L k2 ), the displacement, inclination, and bending moment of the left and right spans of the intersection 131 are equal, so the following boundary conditions are met.

[0046]

number

[0047] Here, the intersection 131(x k1 =L k1 ,x k2 =L k2 Consider the effect of restraining the cables 121 (k=1) and 122 (k=2) by the gripping device 130 at the intersection 131 (x k1=L k1 ,x k2 =L k2 At the intersection 131 (x k1 =L k1 ,x k2 =L k2 ), the forces acting on cables 121 (k=1) and 122 (k=2) are balanced.

[0048] First, intersection 131(x k1 =L k1 ,x k2 =L k2 ) the boundary condition that the displacement directions and displacement amounts of the cables 121 and 122 are equal is expressed as follows:

[0049]

number

[0050] Next, the cables 121 and 122 are held by the holding device 130 at the intersection 131 (x k1 =L k1 ,x k2 =L k2 The balance of forces in the above-mentioned structure will be described with reference to FIG.

[0051] At intersection 131, in the left span of cable k, shear force Q k1 (L k1 ) acts on the right span of cable k, and shear force Q k2 (L k2 ) acts on the cables 121 and 122. At the intersection 131, these shear forces are balanced. Therefore, when the cables 121 and 122 are held by the holding device 130 at the intersection 131, the cross section 131 (x k1 =L k1 ,x k2 =L k2 ) the following boundary conditions are obtained for the balance of forces at

[0052]

number

[0053] The first term on the left side of "Equation 8" represents the force acting on intersection 131 on cable 121, and the second term represents the force acting on intersection 131 on cable 122. The left side of "Equation 8" represents the sum of the forces acting on intersection 131 of cables 121, 122. "Equation 8" represents a state in which the sum of the forces acting on intersection 131 of cables 121, 122 is equal to zero, that is, a state in which the forces are balanced.

[0054] The determinant obtained by applying the boundary condition equation in "Equation 5" above to the general solution equation in "Equation 4" is shown below.

[0055]

number

[0056] Moreover, the boundary condition equations for the displacement and bending moment in the above "Equation 6" are expressed by the following determinant:

[0057]

number

[0058] This determinant (Number 10) can be expressed as follows using the general solution equation of Number 4 and the second derivative of this general solution equation.

[0059]

number

[0060] By substituting the above "Number 9" into "Number 11", we obtain the following relational equation.

[0061]

number

[0062] The matrix F in the above formula (12) kd Using this, the number 10 can be rewritten as follows:

[0063]

number

[0064] Next, the first derivative of the general solution equation of "Mathematical formula 4" is expressed as follows.

[0065]

number

[0066] By substituting the determinant of "Number 9" into "Number 14", we obtain the following relationship.

[0067]

number

[0068] Matrix H of "Number 15" kd Using this, the boundary condition for the slope of “Equation 6” is expressed as follows:

[0069]

number

[0070] By substituting the equation from "Number 13" into "Number 16", we obtain the following equation.

[0071]

number

[0072] Based on "Equation 17", the following relational expression is obtained:

[0073]

number

[0074] Next, the general solution of "Equation 4" is expressed using a matrix as follows:

[0075]

number

[0076] By substituting "Number 9" into "Number 19", we obtain the following relationship.

[0077]

number

[0078] Using "Mathematical Expression 20", the above-mentioned "Mathematical Expression 7" (the equation for the boundary condition related to the displacement at the intersection 131) is expressed as follows.

[0079]

number

[0080] By substituting "Number 18" into "Number 21", we obtain the following relationship.

[0081]

number

[0082] Under the assumption that the displacement at intersection 131 is not zero, Equation (22) above can be rewritten as follows:

[0083]

number

[0084] Next, the third differential of the general solution equation of "Number 4" is expressed as follows.

[0085]

number

[0086] By substituting "Number 9" into "Number 24", we obtain the following relationship.

[0087]

number

[0088] Matrix J of "Number 25" kd Using this, the equation in the curly brackets in "Number 8" (the equation for the boundary condition related to the balance of forces) can be rewritten as follows:

[0089]

number

[0090] By substituting "Number 13" into "Number 26", "Number 26" can be transformed as follows.

[0091]

number

[0092] By substituting "number 18" into "number 27", "number 27" can be transformed as follows.

[0093]

number

[0094] Based on "Number 28", "Number 8" (the equation for the boundary condition related to the balance of forces) can be rewritten as follows.

[0095]

number

[0096] By substituting "Number 29" into "Number 23", we obtain the following relationship.

[0097]

number

[0098] For "number 30" to have any solution other than the trivial one, the value inside the braces must be zero. This gives us the following relation:

[0099]

number

[0100] Since "Number 31" contains hyperbolic functions, in order to prevent problems such as loss of digits, the numerator and denominator of the first term of "Number 31" are written as "m 11 " and divide the numerator and denominator of the second term by "m 21 " As a result of this process, the number 31 is transformed into the following:

[0101]

number

[0102] The first term of "number 32" is represented as "fun1" and the second term is represented as "fun2".

[0103]

number

[0104] When each term of fun1 is simplified and processed to prevent problems such as cancellation of significant digits, each term of fun1 is expanded as follows.

[0105]

number

[0106] In addition, "Na nm11 " "Na nm12 " "Na Fm11 " and "Na Fm12 " is expressed as follows:

[0107]

number

[0108]

number

[0109]

number

[0110]

number

[0111]

number

[0112]

number

[0113]

number

[0114]

number

[0115] "Na nm11 " "Na nm12 " "Na Fm11 " and "Na Fm12 Using ", the above "fun1" can be expressed as follows:

[0116]

number

[0117] Here, the rotational spring stiffness r at both ends of the cable k is k is defined as follows:

[0118]

number

[0119] In the above "Equation 44", the rotational spring stiffness r k The closer to zero is, the closer both ends of the cable k are to being supported at the free ends. On the other hand, the rotational spring stiffness r k The closer to 1, the closer both ends of cable k are to the fixed ends.

[0120] For "fun1" in "Number 43", the rotational spring stiffness r 1 When is less than 1, and the rotational spring stiffness r 1 If we distinguish between when fun1 is equal to 1 and when fun2 is equal to 2, then fun1 can be expressed as follows. Note that the rotational spring stiffness r 1 When is equal to 1, P 1 becomes infinite. In order to avoid calculations involving infinity, the rotational spring stiffness r 1 A distinction is made depending on the value of .

[0121]

number

[0122] For "fun2" in "Number 43", the rotational spring stiffness r 2 When is less than 1, and the rotational spring stiffness r 2 If we distinguish between when is equal to 1 and when is equal to 2, then "fun2" can be expressed as follows.

[0123]

number

[0124] "q" in "Number 45" and "Number 46" k0 ", "q k1 ", "q k2 ", "q k2 ", "s k0 ", "s k1 ", "s k2 " and "s k2 " is expressed as follows:

[0125]

number

[0126]

number

[0127]

number

[0128]

number

[0129]

number

[0130]

number

[0131]

number

[0132]

number

[0133]

number

[0134]

number

[0135]

number

[0136] Using the above-defined “fun1” and “fun2”, the above “Number 31” can be rewritten as follows:

[0137]

number

[0138] The denominators of “fun1” and “fun2” (see “Equation 45”) are represented as “fun3” and “fun4”, respectively, as shown in the following equations.

[0139]

number

[0140] When "fun3" and "fun4" become zero, the above-mentioned "Equation 58" is no longer valid, so "Equation 58" is multiplied by the product of "fun3" and "fun4" as follows. Note that "fun3" takes a value of zero when the amplitude of cable 121 becomes zero at intersection 131, and "fun4" takes a value of zero when the amplitude of cable 122 becomes zero at intersection 131. By multiplying "Equation 58" by the product of "fun3" and "fun4", it is possible to include a case where the amplitude at intersection 131 becomes zero when one of cables 121, 122 does not vibrate at all while the other cable only vibrates.

[0141]

number

[0142] The formula "60" can be expressed as the formula for the i-th mode as follows. In the formula below, the mode order i is expressed as a superscript. The formula below is normalized by dividing it by the values ​​of "fun3" and "fun4" of the first mode. In this embodiment, the formula below is used as the calculation standard formula.

[0143]

number

[0144] "Number 61" is shown as an equation in which the function on the left side is equal to zero. As described above, "Number 61" is set based on "Number 8" which represents the state of balance of forces at the intersection 131. When "Number 61" is satisfied, the forces at the intersection 131 are in balance.

[0145] The function on the left side of "Equation 61" includes the following constants and variables (see "Equation 4", "Equation 5", "Equation 45" to "Equation 57" and "Equation 59"), and the calculation standard formula of "Equation 61" expresses the relationship between the following constants and variables. Note that the function on the left side of "Equation 61" does not include the mode order i as a variable. Total length of cable k: L k Position of intersection 131 (i.e., length of span of cable k): L k1 ,L k2 Cable density: ρ k Cross-sectional area of ​​cable k: A k Measured natural frequency of cable k: f k i Cable tension: T k · Bending stiffness of cable k: E k Ik Rotational spring stiffness: K k

[0146] (Tension T k (Formula for calculating etc.) The function on the left side of the calculation formula in "Number 61" is the tension T k Formula G for calculating 1 i It is used as.

[0147]

number

[0148] Formula G for "Number 62" 1 i By substituting values ​​for the constants and variables in the formula G 1 i The calculation value of is calculated. 1 i The closer the calculated value is to the value of the calculation formula in "Number 61" (i.e., zero), the better the calculation formula G 1 i The value substituted into is considered to be close to the true value when the calculation formula of "Number 61" is satisfied. 1 i The calculated value is compared with the value of the calculation standard formula in "Number 61" (i.e., zero), and the tension T k For this comparison, the following formula G 1 i The sum of squares of is set.

[0149]

number

[0150] Arithmetic expression G 1 i If the sum of the squares of is close to zero, then the formula G 1 iIt can be seen that the value substituted into is close to the true value when the calculation formula of "Number 61" is satisfied. 1 i Using the sum of squares, the tension T k A specific method for calculating the above will be described below with reference to FIG.

[0151] (Tension T k (Calculation method for etc.) The following structural data for cable k is obtained (step S105): 1 i This is substituted as a fixed value into the sum of squares (Equation 63). Total length of cable k: L k Position of intersection 131 (i.e., length of span of cable k): L k1 ,L k2 Cable density: ρ k Cross-sectional area of ​​cable k: A k

[0152] After acquiring the structural data, as shown in FIG. 1, acceleration sensors 141 and 143 are attached to the cables 121 and 122, and a data collector 160 is connected to the acceleration sensors 141 and 143. Then, the actual measured values ​​f of the natural frequencies of the cables 121 and 122 for a plurality of vibration modes are k i An actual measurement process (steps S110 to S120 in FIG. 4) is performed to obtain the above information.

[0153] In the actual measurement step, the cables 121 and 122 are vibrated in an out-of-plane direction (step S110). The acceleration of the vibration generated in the cables 121 and 122 is measured by the acceleration sensors 141 and 143. The measured acceleration of the vibration is recorded as a time history response value in the data collection device 160 (step S115). The data collection device 160 performs a Fourier transform on the time history response value, and calculates the actual value of the natural frequency f from the peak value of the data after the Fourier transform. k i is acquired (step S120).

[0154] As a result of the above-mentioned Fourier transform, data such as that shown in Figure 5 is obtained. The frequency at which the vibration intensity peak appears is the measured natural frequency f k 1 ~f k 6 The formula G is obtained as 1 i does not include the variable for mode number i, so the formula G 1 i For the purpose of the substitution process (described later), the measured value of the natural frequency f k 1 ~f k 6 It is not necessary to obtain the frequency f in correspondence with the mode number i. Therefore, for example, as shown in Fig. 5, the frequencies at which the peaks appear are obtained in ascending order of the measured natural frequency f k 1 ~f k 6 It may be obtained as.

[0155] The structural data acquired in step S105 and the actual measured value f of the natural frequency acquired in step S120 k 1 ~f k 6 The data is calculated using the formula G 1 i The sum of squares (number 63) is substituted (calculation step). As a result, the calculation formula G 1 i The sum of the squares of (Equation 63) is the tension T of cable k. k , bending stiffness E of cable k k I k and rotational spring stiffness K k It can be treated as a function that contains variables. 1 i The sum of squares of (Equation 63) and the structural data and the measured value of the natural frequency f k 1 ~f k 6 After inputting the data, the tension T in cable k k , bending stiffness E k I k and rotational spring stiffness Kk A search process (calculation step) is performed to find an optimal solution (step S125).

[0156] Tension T k , bending stiffness E k I k and rotational spring stiffness K k The search process for finding the optimal solution of the formula G will be described with reference to FIG. 1 i 63 is a conceptual graph of the sum of squares of (Equation 63). k , bending stiffness E of cable k k I k and rotational spring stiffness K k The optimal solution is calculated based on the MultiStart method.

[0157] The horizontal axis of Fig. 6 is tension T k , bending stiffness E k I k or rotational spring stiffness K k The graph in FIG. 6 is drawn as a two-dimensional coordinate system, but the calculation in the search process is a four-dimensional coordinate system (calculation formula G 1 i Sum of squares of tension T k , bending stiffness E k I k and rotational spring stiffness K k This is carried out on four axes:

[0158] Tension T k , bending stiffness E k I k and rotational spring stiffness K k N initial values ​​are set for the arithmetic expression G. FIG. 6 shows the first to sixth initial values. The set initial values ​​are 1 i The sum of squares (number 63) is substituted into the formula G 1 i The tension T is substituted into the sum of squares (63). k The value of is the candidate value of the tension estimated to be acting on cable k. 1 i The bending stiffness E is substituted into the sum of squares (Equation 63).k I k The value of is the candidate value of the bending stiffness of cable k. 1 i The rotational spring stiffness K is substituted into the sum of squares (Equation 63). k The values ​​of are candidates for the rotational spring stiffness of the rotational springs inserted at both ends of the cable k. These candidates (i.e., substituted values) are referred to as "tension candidate value", "bending stiffness candidate value" and "spring stiffness candidate value" in the following description.

[0159] The initial value is entered, and the calculation formula G 1 i When the calculated value of the sum of squares (Equation 63) is obtained, at least one of the tension candidate value, bending stiffness candidate value, and spring stiffness candidate value is changed, and based on these new combinations, the calculation formula G 1 i The sum of squares (63) is calculated. The formula G obtained from the new combination 1 i The sum of squares (number 63) of 1 i It is judged whether the sum of squares (63) of is less than the value of G. 1 i Based on the degree of reduction in the calculated value of the sum of squares (Equation 63), a new combination of the tension candidate value, bending stiffness candidate value, and spring stiffness candidate value is repeatedly set, and the calculation formula G 1 i The minimum value of the sum of squares (Equation 63) is searched for.

[0160] Arithmetic expression G 1 iFour minimum values ​​(referred to as the "first minimum value", "second minimum value", "third minimum value", and "fourth minimum value" in the following description) of the sum of squares (Equation 63) of are shown in Fig. 6. With respect to the graph in Fig. 6, when the search is started from the first and second initial values, the first minimum value can be obtained. When the search is started from the third initial value, the second minimum value can be obtained. When the search is started from the fourth and fifth initial values, the third minimum value can be obtained. When the search is started from the sixth initial value, the fourth minimum value can be obtained.

[0161] The smallest one is found from among the multiple minimum values ​​obtained by the above-mentioned search process. The tension candidate value, bending stiffness candidate value, and spring stiffness candidate value when the smallest minimum value is obtained are the tension T k , bending stiffness E k I k and rotational spring stiffness K k Regarding the graph of FIG. 6, since the third minimum value is the smallest, the set of tension candidate value, bending stiffness candidate value, and spring stiffness candidate value used in the calculation of the third minimum value is determined as the tension T k , bending stiffness E k I k and rotational spring stiffness K k is determined as the calculated value.

[0162] It is expected that the peaks in the data after Fourier transformation shown in Figure 5 will be overlooked due to noise. For example, as shown in Figure 7, the measured value of the natural frequency f k 4 If the peak corresponding to is overlooked, the measured natural frequency f k 5 ,f k 6 The natural frequency obtained as is the actual measured value of the natural frequency f k 4 ,f k 5 In this case, the formula G 1 iSince does not include the mode number i, it is not necessary to substitute the measured value of the natural frequency acquired in step S120 in correspondence with the mode number i. Therefore, the measured value of the natural frequency f k 4 Even if the peak corresponding to mode i is overlooked, the measured value of the natural frequency f k i Therefore, there is no possibility of miscalculation due to the mismatch of tension T k , bending stiffness E k I k and rotational spring stiffness K k can be calculated with high accuracy.

[0163] Arithmetic expression G 1 i is based on the model shown in Fig. 2, in which a rotational spring is inserted at both ends of the cable k. The characteristics of the rotational spring are given by the rotational spring stiffness K k The rotational spring stiffness K k If is large, both ends of the cable k are close to the fixed ends, and conversely, the rotational spring stiffness K k If is small, both ends of the cable k are close to being free ends. k In the search process (step S125 in FIG. 4, FIG. 6), the tension T k and bending stiffness E k I k If such a search process is performed, the tension T k Therefore, the tension T k The accuracy of calculated values ​​such as these will be improved.

[0164] In the process shown in FIG. 4, the combination of the tension candidate value, bending stiffness candidate value, and spring stiffness candidate value when the minimum value obtained in the search process (step S125) is the tension T k , bending stiffness E k I k and rotational spring stiffness K k In addition to this process, the tension T kFor example, as shown in FIG. 8, the calculation formula G obtained by the search process in step S125 may be 1 i The minimum value of the sum of squares of the formula G may be compared with a predetermined threshold value (step S130). 1 i If the minimum value of the sum of squares of is less than the threshold value (step S130: Yes), the set of tension candidate value, bending stiffness candidate value, and spring stiffness candidate value at this time is the tension T k , bending stiffness E k I k and rotational spring stiffness K k It is determined as the calculated value of . 1 i If the minimum value of the sum of squares of is equal to or greater than the threshold value (step S130: No), the search range may be changed by changing the initial value shown in FIG. 6 (step S135), and the search process (step S125) may be performed again. 1 i The search range is changed (step S135) and the search process (step S125) is repeated until the minimum value of the sum of squares of the tension T is smaller than the threshold value. k etc. are calculated.

[0165] 8, if high calculation accuracy is desired, a small threshold value should be set, whereas if high calculation accuracy is not required, a large threshold value should be set.

[0166] <Second embodiment> Tension T k A calculation standard equation used for the calculation of the above may be set based on the vibration shape of the cable k in each vibration mode. In order to measure the vibration shape of the cable k in each vibration mode, for example, as shown in FIG. 9, two acceleration sensors 141, 142 may be attached to a span 171 of the cable 121. In this case, the data collection device 160 is connected to these acceleration sensors 141, 142 so as to be able to receive data from these acceleration sensors 141, 142. In the following description, the attachment position of the acceleration sensor 141 will be referred to as "x 11=u 11 ” and the mounting position of the acceleration sensor 142 is represented by “x 11 =u 12 " is expressed as

[0167] A general solution of the vibration equation (Equation 3) for cable 121 is expressed as follows: Note that the general solution below is obtained by expressing "k" in the above-mentioned "Equation 4" as "1".

[0168]

number

[0169] Moreover, the boundary condition equations of "Equation 5" and "Equation 6" above can be rewritten as follows for cable 121:

[0170]

number

[0171] Based on the boundary conditions in (65), the integral constant C in the general solution of (64) 1d1 ~C 1d4 The relationship between them is expressed as follows:

[0172]

number

[0173] In this embodiment, the vibration shape of the cable 121 is the issue, so the integral constant C 1d1 ~C 1d4 The size of is not an issue. Therefore, to simplify the above "number 66", we use "C 112 =m 12 " This means that the number 66 can be rewritten as follows:

[0174]

number

[0175] Based on the number 67, the number 64 can be rewritten as follows:

[0176]

number

[0177] Following the example of the above-mentioned "number 45", "number 68" can be expressed as "r 1 <1, and "r 1 If we distinguish between the cases where r = 1 and where r = 2, then we can rewrite "Number 68" as follows. Since we are solving the constraint that the Fourier amplitude ratio, not the Fourier amplitude, must be equal between the measured value and the theoretical value, it is the Fourier amplitude ratio that is meaningful, not the Fourier amplitude itself. 1 = 1, P becomes infinity 1 2 The term is "r" in "Number 69" below. 1 = 1". Note that X in "Number 68" is dropped from the equation. 0 (x 11 ),X 1 (x 11 ),X 2 (x 11 ) is defined in "Number 70" to "Number 72".

[0178]

number

[0179]

number

[0180]

number

[0181]

number

[0182] "W" in "Number 69" 11 (x 11 ) corresponds to the Fourier amplitude obtained by applying a Fourier transform process to the data obtained from the acceleration sensors 141 and 142. In order to make the data easier to handle, the absolute value of the Fourier amplitude, i.e., "W 11 (x 11 In the following explanation, the absolute value of φ i t The theoretical formula for the absolute value of the Fourier amplitude at the mounting positions of the acceleration sensors 141 and 142 is given below.

[0183]

number

[0184] The theoretical formula for "Number 73" is tension T k , bending stiffness E k I k , rotational spring stiffness K k and the natural frequency f of multiple modes k i (see Number 4, Number 5, Number 68 and Number 69).

[0185] The constraint equation that the difference between the ratio of the absolute values ​​of the theoretical values ​​obtained from the theoretical equation of "Equation 73" and the ratio of the absolute values ​​of the actual measured values ​​of the Fourier amplitudes obtained by applying a Fourier transform process to the data obtained from the acceleration sensors 141 and 142 (i.e., the Fourier amplitude ratio) is equal to zero is shown below. Note that in the constraint equation below, cases are distinguished so that the ratio of the absolute values ​​of the Fourier amplitudes is 1 or less.

[0186]

number

[0187] By carrying out the same calculation process as in "Equation 60" and "Equation 61" in consideration of the case where the deflection at the intersection 131 becomes zero, "Equation 74" can be rewritten as follows.

[0188]

number

[0189] In the span 171, when j (j ≥ 2) acceleration sensors are installed, the installation positions of these acceleration sensors are defined as "u 1j " and "Number 75" can be rewritten as follows and used as the calculation standard formula.

[0190]

number

[0191] "Equation 76" is shown as an equation where the function on the left hand side is equal to zero. The function on the left hand side of "Equation 76" includes the following constants and variables. Note that the function on the left hand side of "Equation 76" does not include the mode number i as a variable. Total length of cable 121: L 1 Position of intersection 131 (i.e., length of spans 171, 172 of cable 121): L 11 ,L 12 Density of cable 121: ρ 1 Cross-sectional area of ​​cable 121: A 1 Measured natural frequency of cable 121: f 1 i Tension of cable 121: T 1 · Bending stiffness of cable 121: E 1 I 1 Rotational spring stiffness: K 1

[0192] (Tension T 1 (Formula for calculating etc.) The function on the left side of the calculation formula of "Number 76" is the tension T 1 Formula G for calculating 2 ij It is used as.

[0193]

number

[0194] The formula for "number 77" G 2 ij By substituting values ​​for the constants and variables in the formula G 2 ij The value of is calculated. 2 ij The closer the value calculated from the formula "76" is to the value of the calculation standard formula (i.e., zero), the better the calculation formula G 2 ij The value substituted into is considered to be close to the true value when the calculation formula of "Number 76" is satisfied. 2 ij The tension T is calculated by comparing the calculated value with the value of the calculation standard formula in "Number 76" (i.e., zero). 1 For this comparison, the following formula G 2 ij The sum of squares of is set.

[0195]

number

[0196] Arithmetic expression G 2 ij If the sum of the squares of is close to zero, then the formula G 2 ij It can be seen that the value substituted into is close to the true value when the calculation formula of "Number 75" is satisfied. 2 ij Using the sum of squares, the tension T 1 A specific method for calculating the above will be described below with reference to FIG.

[0197] (Tension T 1 (Calculation method for etc.) First, the following structure data regarding the cable 121 is obtained (step S106). The following structure data is calculated using the formula G2 ij This is substituted as a fixed value into the sum of squares (Equation 77). Total length of cable 121: L 1 Position of intersection 131 (i.e., length of spans 171, 172 of cable 121): L 11 ,L 12 Density of cable 121: ρ 1 Cross-sectional area of ​​cable 121: A 1

[0198] After acquiring the structural data, as shown in FIG. 9, acceleration sensors 141, 142, etc. are attached to the cable 121, and a data collection device 160 is connected to the acceleration sensors 141, 142, etc. Then, the actual measured values ​​f of the natural frequencies of the cables 121, 122, etc. are collected for a plurality of vibration modes. 1 i An actual measurement process (steps S111 to S121 in FIG. 9) is performed to obtain the above information.

[0199] In the actual measurement process, the tension T k Similarly to the calculation methods for the above, the cables 121 and 122 are vibrated in the out-of-plane direction (step S111), and the acceleration of the vibration generated in the cable 121 is measured by the acceleration sensors 141 and 142. The measured acceleration of the vibration is recorded as a time history response value in the data collection device 160 (step S116). The data collection device 160 performs a Fourier transform on the time history response value, and calculates the actual value of the natural frequency f from the peak value of the data after the Fourier transform. 1 i and the measured value of the Fourier amplitude φ i m (u 1j ) is acquired (step S121).

[0200] As a result of the above-mentioned Fourier transform, for example, data as shown in Fig. 11 is obtained. Fig. 11(a) shows data after Fourier transform of the time history response value obtained from the acceleration sensor 141 (x 11 =u 11 ). Figure 11(b) shows the "x11 =u 1j This is data obtained by Fourier transform of the time history response values ​​obtained from the acceleration sensor 142 etc. attached at the attachment position where "

[0201] In the data in Fig. 11, the measured Fourier amplitude φ i m (u 1j ) is the measured value of the Fourier amplitude φ i m (u 11 ) is smaller than the Fourier amplitude φ i m (u 1j ) as the denominator, and the Fourier amplitude φ i m (u 11 ) is used as the numerator, and the ratio of the measured Fourier amplitudes is calculated for each mode number i.

[0202] The structural data acquired in step S106 and the actual measured value f of the natural frequency acquired in step S121 1 i and the ratio of the measured Fourier amplitude (=φ i m (u 11 ) / φ i m (u 1j The data in the formula G 2 ij The sum of squares (number 77) is substituted into the formula G 2 ij The sum of the squares of (Number 77) is the tension T of cable 121. 1 , bending stiffness E of cable 121 1 I 1 and rotational spring stiffness K 1 It can be treated as a function that contains variables. 2 ij The sum of squares of (Equation 77) and the measured value of the natural frequency f 1 i After inputting the data of the ratio of the measured values ​​of the Fourier amplitudes, the tension T of the cable 121 is 1A search process is performed to obtain an optimal solution such as (step S126). This search process is performed based on the MultiStart method, as in the first embodiment (see FIG. 6). That is, in the search process, 1 , bending stiffness E 1 I 1 and rotational spring stiffness K 1 While changing the candidate value of the formula G 2 ij The sum of squares of is calculated. The tension T that minimizes the sum of squares in the search range is 1 , bending stiffness E 1 I 1 and rotational spring stiffness K 1 The candidate value of tension T 1 , bending stiffness E 1 I 1 and rotational spring stiffness K 1 is determined as:

[0203] As in the first embodiment, the calculation formula G 2 ij does not include the mode number i, it is not necessary to substitute the measured value of the natural frequency acquired in step S121 in correspondence with the mode number i. Therefore, the mode number i and the measured value of the natural frequency f 1 i Therefore, there is no possibility of miscalculation due to the mismatch of tension T 1 , bending stiffness E 1 I 1 and rotational spring stiffness K 1 can be calculated with high accuracy.

[0204] Arithmetic expression G 2 ij But the rotational spring stiffness K 1 is treated as a variable in the search process (step S126). 1 and bending stiffness E 1 I 1 is calculated taking into consideration the support state of both ends of the cable 121 from a state close to the fixed end to a state close to the free end. 1 The accuracy of calculated values ​​such as these will be improved.

[0205] 9, the acceleration sensors 141 and 142 are attached to span 171 (the left span) of the cable 121. Alternatively, the acceleration sensors 141 and 142 may be attached to span 172 (the right span) of the cable 121. If the acceleration sensors 141 and 142 are attached to either span 171 or 172 of the cable 121, the tension T 1 etc. can be calculated.

[0206] Tension T of cable 122 2 , bending stiffness E 2 I 2 and rotational spring stiffness K 2 In order to calculate the tension T of the cable 122, multiple acceleration sensors may be attached to the span 173 or span 174 of the cable 122. In this case, the tension T of the cable 122 is calculated based on the time history response data obtained from the multiple acceleration sensors attached to the cable 122. 2 It will be possible to calculate the following:

[0207] In the calculation method of the second embodiment, additional processing (similar to steps S130 and S135 in FIG. 8) may be performed to ensure the calculation accuracy. 2 ij Set a threshold for the minimum value of the sum of squares of G 2 ij Based on a comparison of the minimum sum of squares of , and a threshold, it may be determined whether to continue the search process.

[0208] The calculation methods of the first and second embodiments are combined to calculate the tension T k In this case, in the search process, the tension T that minimizes the calculated value obtained from the following sum of squares formula is k , bending stiffness E k I k and rotational spring stiffness K k The candidate value of tension T k , bending stiffness E k I k and rotational spring stiffness K k is determined as:

[0209]

number

[0210] In the above-described embodiment, the linear body is a cable 121 or 122. Alternatively, the linear body may be a steel rod or other linear member. [Industrial Applicability]

[0211] The techniques described in relation to the above embodiments are well suited for investigating tensions and stiffnesses acting on a variety of linear bodies that can be modelled as one-dimensional beams. [Explanation of symbols]

[0212] 121, 122... Cable (linear body) 130····································· Gripping device 131 Intersection

Claims

1. A method for calculating tension, bending rigidity, and rotational rigidity at both ends of two linear bodies held by a holding device so as to cross each other, comprising the steps of: a measuring step of obtaining actual measured values ​​of natural frequencies of multiple modes for each of the two linear bodies based on vibration of the two linear bodies; a calculation step of calculating the tension, the bending stiffness, and the rotation stiffness using a calculation standard equation set using boundary conditions that represent that an intersection of the two linear bodies is gripped by the gripping device and that both ends of each of the two linear bodies have the rotation stiffness, and the actual measured values ​​of the natural frequencies of the multiple modes, the calculation standard formula is expressed as a formula in which a function including variables of the tension, the bending stiffness, the rotation stiffness, and the natural frequencies of the multiple modes is equal to a predetermined value, In the calculation step, Substituting the candidate values ​​set for each of the tension, the bending stiffness, and the rotational stiffness, and the actual measured values ​​of the natural frequencies of the multiple modes into corresponding variables of the function, respectively, to obtain a calculated value of the function; A calculation method, comprising: calculating the tension, the bending stiffness, and the rotational stiffness based on a comparison between the acquired calculated value and the predetermined value.

2. The calculation method according to claim 1 , wherein the calculation criteria formula expresses the relationship between the natural frequencies, the tension, the bending stiffness and the rotational stiffness of the multiple modes without including a modal order.

3. The calculation method according to claim 1 or 2, wherein the boundary conditions include a condition indicating that the directions and amounts of displacement of the two linear bodies at the intersection are equal.

4. the function of the calculation standard equation expresses a sum of a force acting on the intersection of one of the two linear bodies and a force acting on the intersection of the other linear body, using variables of the natural frequencies of the multiple modes, the tension, the bending rigidity, and the rotational rigidity, The calculation criterion formula is expressed as a formula for which the function is equal to a value of zero, In the calculation step, Substituting the candidate values ​​of the tension, the bending stiffness, and the rotational stiffness, and the actual measured values ​​of the natural frequencies of the multiple modes into corresponding variables of the functions, respectively, to obtain the calculated values; The method according to claim 1 , further comprising the steps of: calculating the tension, the bending stiffness and the rotational stiffness based on a comparison between the obtained calculated value and a value of zero.

5. In the actual measurement step, Fourier amplitudes at the natural frequencies of the multiple modes corresponding to the actual measured values ​​of the natural frequencies of the multiple modes are measured at two mutually different positions on each of the two linear bodies, and an actual measured value of a Fourier amplitude ratio, which is a ratio of the actual measured values ​​of the Fourier amplitudes obtained at the two positions, is obtained; the function of the calculation standard equation is set to represent a difference between a theoretical value obtained from a theoretical equation of a Fourier amplitude ratio expressed as a function of the tension, the bending rigidity, the rotational rigidity, and the natural frequencies of the multiple modes, and the actual measured value of the Fourier amplitude ratio; The calculation standard formula is set to express a relationship in which the difference between the theoretical value of the Fourier amplitude ratio and the actual measured value of the Fourier amplitude ratio is equal to a value of zero, In the calculation step, the actual value of the Fourier amplitude ratio acquired in the actual measurement step is substituted into the term of the actual value of the Fourier amplitude ratio in the function, and the candidate values ​​of the tension, the bending rigidity, and the rotational rigidity, and the actual values ​​of the natural frequencies of the multiple modes are substituted into the theoretical formula, thereby obtaining the difference between the actual value of the Fourier amplitude ratio and the theoretical value of the Fourier amplitude ratio as the calculated value; The method according to claim 1 , further comprising the step of calculating the tension, the bending stiffness and the rotational stiffness based on a comparison of the calculated value of the difference with the value of zero.

6. In the calculation step, Repeating the process of substituting another candidate value set for at least one of the tension, the bending stiffness, and the rotational stiffness, and the actual measured values ​​of the natural frequencies of the multiple modes into the function to obtain another calculated value, thereby obtaining a plurality of calculated values; The calculation method according to claim 1 , wherein a candidate value that is closest to the predetermined value among the plurality of calculated values ​​is determined as the calculated values ​​of the tension, the bending stiffness, and the rotational stiffness.

7. In the calculation step, 6. The calculation method according to claim 1, further comprising repeating an assignment process of assigning another candidate value set for at least one of the tension, the bending stiffness, and the rotational stiffness, and the actual measured values ​​of the natural frequencies of the multiple modes to the function, until a difference between the calculated value and the predetermined value becomes less than a predetermined threshold value.

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